Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11763161 | C2 | semidirect |
| 4. #11763113 | C2 | semidirect |
| 7. #11763019 | C2 | semidirect |
| 8. Q8×#3622 | C2 | semidirect |
| 9. C4×#63231 | C2 | semidirect |
| 11. C17×#557 | C2 | semidirect |
| 112. #557 | D17 | semidirect |
| 156. C17 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763532 | 2 |
| #11763166 | 2 |
| #11763161 | 2 |
| #11763113 | 2 |
| #11763086 | 2 |
| #11763031 | 2 |
| #11763019 | 2 |
| Q8×#3622 | 2 |
| C4×#63231 | 2 |
| C4×#63230 | 2 |
| C17×#557 | 2 |
| #3364 | 17 |